If you keep Apache itself up-to-date then typically speaking no. There is always a reason to be on the lookout and <insert generic speech about security concern

If you keep Apache itself up-to-date then typically speaking no. There is always a reason to be on the lookout and <insert generic speech about security concerns here>, but static files are - well - static. Not much to mess with there. If you choose to do smart things like caching and such, that opens a whole new can of worms, but basic "this is my HTML page" stuff is typically "not-unsafe" (as opposed to "safe").